Implementing Jet Algorithms A Practical Jet Primer Stephen

Implementing Jet Algorithms: A Practical Jet Primer Stephen D. Ellis University of Washington West Coast LHC Theory Network UC Davis December 2006 S. D. Ellis WC LHC Thy. Net. Work December 2006

Outline: • Jet Jargon • Big Picture Jet Goals for LHC • Cone Details & Lessons from the Tevatron • k. T – the hope for the future? • Jets & BSM issues (at the LHC) • Summary See Te. V 4 LHC QCD Report hep-ph/610012 S. D. Ellis WC LHC Thy. Net. Work December 2006 2

Jet Jargon: • IR safety – Dave : Thy - cancel singularities, Exp – lower sensitivity to soft stuff • • • Cone algorithm – Dave; “stable” cones & “fixed” geometry Split/merge issue – Overlapping cones – Dave Seeds – IR sensitivity – Dave : fix in data, NOT apply to theory Rsep – match NLO Pert Thy to experiment (does NOT break cone) JETCLU (Run I CDF) & Ratcheting Mid. Point Cone Algorithm – A Fix for Run II : Always look for stable cone between 2 stable cone • Dark Towers – Dave’s “Walls”: Energetic towers not in any stable cone • Search Cone Algorithm – a CDF NOT fix in Run II • k. T algorithm – pairwise reconstruction, softest first – Dave • Underlying Event (UE) and the k. T algorithm • Pile-up – collisions overlapping in time S. D. Ellis WC LHC Thy. Net. Work December 2006 3

The Goal at the LHC is a 1% (Precision) Description of Strong Interaction Physics (where Tevatron Run I is ~ 10%) To this end we want to precisely map • physics at 1 meter, i. e. , what we can measure in the detector, e. g. , E(y, ) On To • physics 1 fermi, i. e. , what we can calculate with small numbers of partons, leptons and gauge bosons as functions of E, y, We “understand” what happens at the level of short distance partons and leptons, i. e. , perturbation theory is simple, can reconstruct masses, etc. S. D. Ellis WC LHC Thy. Net. Work December 2006 4

“SOLUTION”: associate “nearby” hadrons or partons into JETS via ALGORITHMS, i. e. , rules that can be applied to data and theory • Cone Algorithms, e. g. , Snowmass, based on “fixed” geometry (well suited to hadron colliders with UEs) • k. T Algorithm, based on pairwise merging, nearest, lowest p. T first (familiar at e+e- colliders), tends to “vacuum up” soft particles Render Pert. Thy IR & Collinear Safe But mapping of hadrons to partons can never be 1 to 1, event-by-event! Colored states ≠ singlet states! S. D. Ellis WC LHC Thy. Net. Work December 2006 6

Goals of IDEAL ALGORITHM (Motherhood) • Fully Specified: including defining in detail any preclustering, merging, and splitting issues • Theoretically Well Behaved: the algorithm should be infrared and collinear safe (and insensitive) with no ad hoc clustering parameters (e. g. , RSEP) • Detector Independence: there should be no dependence on cell type, numbers, or size • Order Independence: The algorithms should behave equally at the parton, particle, and detector levels. • Uniformity: everyone uses the same algorithms S. D. Ellis WC LHC Thy. Net. Work December 2006 7

Defining a Jet with Algorithm- • Start with a list of particles (4 -vectors) and/or calorimeter towers (energies and angles) • End with lists of particles/towers, one list for each jet • And a list of particles/towers not in any jet – the spectators – remnants of the initial hadrons not involved in the short distance physics (but there must be some correlations and ambiguity) S. D. Ellis WC LHC Thy. Net. Work December 2006 8

Fundamental Issue – Compare Experiments to each other & to Theory Warning: We should all use the same algorithm!! (as closely as humanly possible), i. e. both ATLAS & CMS (and theorists). This is NOT the case at the Tevatron, even in Run II!! And should NOT be the case if experiments use seeds, etc. – CORRECT for these in data analysis (already correct for detector effects, hadronization) S. D. Ellis WC LHC Thy. Net. Work December 2006 9

Observations: • Iterative Cone Algorithm Has detailed issues (merge/split, seeds, dark towers), which only became clear with serious study (and this is a good thing) And now we know (most of) the issues and can correct for them • The k. T Algorithm May have detailed issues (“vacuum” effect, UE and pile-up sensitivity, . . ), but much less mature experience at hadron colliders We need to find out with the same sort of serious study (history says issues will arise) S. D. Ellis WC LHC Thy. Net. Work December 2006 10

Run I - Snowmass Cone Algorithm • Cone Algorithm – particles, calorimeter towers, partons in cone of size R, defined in angular space, e. g. , ( , ) • CONE center - ( C, C) • CONE i C iff • Energy • Centroid S. D. Ellis WC LHC Thy. Net. Work December 2006 11

• Jet is defined by “stable” cone • Stable cones found by iteration: start with cone anywhere (and, in principle, everywhere), calculate the centroid of this cone, put new cone at centroid, iterate until cone stops “flowing”, i. e. , stable Proto-jets (prior to split/merge) • “Flow vector” unique, discrete jets event-by-event (at least in principle) S. D. Ellis WC LHC Thy. Net. Work December 2006 12

Run I Issues (Life gets more complex): Cone: Seeds – only look for jets under brightest street lights, i. e. , near very active regions problem for theory, IR sensitive at NNLO Stable Cones found by iteration (ET weighted centroid = geometric center) can Overlap, require Splitting/Merging scheme merge if share energy fraction > fmerge parameter Different in different experiments Don’t find “possible” central jet between two well separated proto-jets (partons) S. D. Ellis WC LHC Thy. Net. Work December 2006 14

Cones: Seeds and Sensibility • Tension between desire To Limit analysis time (for experiments) with seeds To Use identical algorithms in data and perturbation theory • Seeds are intrinsically IR sensitive (Mid. Point Fix only for NNLO, not NNNLO) DON’T use seeds in perturbation theory, correct for them in data analysis In theory they are a big deal – IR UNsafety (Yikes)!!!!!! In the data seeds vs seedless is a few % correction (e. g. , lower the Seed p. T threshold) and this is small compared to other corrections – [Run I jets results are meaningful!!] S. D. Ellis WC LHC Thy. Net. Work December 2006 15

To understand these issues consider Snowmass “Potential” • In terms of 2 -D vector or define a “potential” • Extrema are the positions of the stable cones; gradient is “force” that pushes trial cone to the stable cone, i. e. , the flow vector S. D. Ellis WC LHC Thy. Net. Work December 2006 16

(THE) Simple Theory Model - 2 partons (separated by d < 2 R): yield potential with 3 minima – trial cones will migrate to minima from seeds near original partons miss central minimum d , d = separation Smearing of order R S. D. Ellis WC LHC Thy. Net. Work December 2006 17

Numerical issue: • Seeds can mean missed configurations with 2 partons in 1 Jet, NLO Perturbation Theory – d = parton separation, z = p 2/p 1, , Simulate the missed middle cones with Rsep Naïve Snowmass With Rsep No Seed s 2 jet < 10% of cross section here S. D. Ellis WC LHC Thy. Net. Work December 2006 18

Run I Cone Issues (Life gets more complex): 3) Kinematic variables: ET, Snow ≠ ET, CDF ≠ ET, 4 D = p. T (5 % differences) Different in different experiments and in theory 4) • • • Other details – Energy Cut on towers kept in analysis (e. g. , to avoid noise) (Pre)Clustering to find seeds (and distribute “negative energy”) Energy Cut on precluster towers Energy cut on clusters Energy cut on seeds kept 5) Starting with seeds find stable cones by iteration, but in JETCLU (CDF), “once in a seed cone, always in a cone”, the “ratchet” effect S. D. Ellis WC LHC Thy. Net. Work December 2006 19

To address these issues, the Run II Study group Recommended Both experiments use • (legacy) Midpoint Algorithm – always look for stable cone at midpoint between found cones • Seedless Algorithm • k. T Algorithms • Use identical versions except for issues required by physical differences (in preclustering? ? ) • Use (4 -vector) E-scheme variables for jet ID and recombination S. D. Ellis WC LHC Thy. Net. Work December 2006 21

A NEW issue for Iterative Cone Algorithms – DARK TOWERS (Dave’s Walls) • Compare jets found by JETCLU (with ratcheting) to those found by Mid. Point and Seedless Algorithms • “Missed Energy” – when energy is smeared by showering/hadronization do not always find stable cones expected from perturbation theory 2 partons in 1 cone solutions or even second cone Under-estimate ET – new kind of Splashout S. D. Ellis WC LHC Thy. Net. Work December 2006 22

Missed or Dark Towers (not in any stable cone) – How can that happen? (Dave’s issue with “walls”) Results from M. Tönnesmann S. D. Ellis WC LHC Thy. Net. Work December 2006 23

Why Dark towers? Include smearing (~ showering & hadronization) in simple picture, find only 1 stable cone (no midpoint stable cone & dark towers) d S. D. Ellis WC LHC Thy. Net. Work December 2006 24

Compare with smearing: Mid. Point will still miss 2 -in-1 Jets (Rsep < 2) Missing Mid. Point (no C stable cone) Dark towers (no R stable cone) =0 = 0. 1 S. D. Ellis WC LHC Thy. Net. Work December 2006 = 0. 25 25

Proposed Fix with smaller radius Search Cone – Used by CDF • Over compensates with (too) many found stable cones, so use larger f_merge (f_CDF > f_D 0) • (Re)Introduces IR-sensitivity through soft stable search cones (R’ < R) that, when expanded to R, can envelop and merge nearby pairs of energetic partons, which themselves do not correspond to a stable cone (R) • NOT A COMPLETE SOLUTION!! S. D. Ellis WC LHC Thy. Net. Work December 2006 26

Better(? ) - Consider a Dark Tower Correction based on Comparison to p. QCD • Take multiple passes at data 1 st pass jets = found by Cone Algorithm 2 nd pass jets = missed by Cone Algorithm (but found if remove 1 st pass jet) • Merge if in correct region of (d, z) plane (? ) Correct to data! Search Cone Merge 1 & 2 nd pass jets, Rsep = 1. 3 Mid. Point Cone Merge 1 & 2 nd pass jets, Rsep = 2. 0 S. D. Ellis WC LHC Thy. Net. Work December 2006 2 nd Pass Jets after algorithms 27

The k. T Algorithm • Merge partons, particles or towers pair-wise based on “closeness” defined by minimum value of If dij 2 is the minimum, merge pair and redo list; If di 2 is the minimum -> i is a jet! (no more merging for i), 1 parameter D (? ), at NLO R = 0. 7, Rsep = 1. 3 D = 0. 83 • Jet identification is unique – no merge/split stage • Resulting jets are more amorphous, energy calibration difficult (subtraction for UE? ), and analysis can be very computer intensive (time grows like N 3, recalculate list after each merge) But new version (Cacciari & Salam) goes like N ln N (only recalculate nearest neighbors) S. D. Ellis WC LHC Thy. Net. Work December 2006 28

In the future: (comments, not criticisms) • When we look carefully will we find problems and add details ? History says yes! (See below) • The (official? ) k. T webpage has 5 parameters to specify the implementation, resolution variable, combination scheme, etc. • Recall the Cambridge k. T (e+e-) algorithm that added angular ordering to get rid of “junk jets” (resolution variable ordering variable) and “soft-freezing” to reduce mis-clustering S. D. Ellis WC LHC Thy. Net. Work December 2006 29

Jet Algorithm Summary: • Seeds & p. QCD are a bad mix (not IRS). It is better to correct for seeds during the analysis of the data (a small correction) and compare to theory w/o seeds (so no IRS issue) !! • Dark towers are a real 5 - 10% effect, but the search cone fix aggravates the IRS issue – better to recognize as a correction during the analysis of the data (or theory), along with corrections for detector, UE, hadronization, seeds, and missing 2 -in-1 configurations • Compare corrected experimental numbers to p. QCD without seeds and Rsep = 2 • Need serious phenomenology study of the k. T algorithm S. D. Ellis WC LHC Thy. Net. Work December 2006 30

Same Event – slightly different jets Merged jets Dark towers UN Merged jets CDF Legacy Cone Run II Cone Algorithms S. D. Ellis WC LHC Thy. Net. Work December 2006 31

Corrections Cone Seed and Dark Tower corrections current CDF corrections for hadrons → partons KT S. D. Ellis WC LHC Thy. Net. Work December 2006 32

S. D. Ellis WC LHC Thy. Net. Work December 2006 33

Goals at LHC Different Figure of Merit for Jet algorithm? • Find Physics Beyond the Standard Model • Event structure likely different from QCD, more jets? Overlap? Different structure within jets? • Want to select on non-QCD-ness • Highly boosted SM particles – W, Z, top single jet instead of 2 or 3 jets, focus on substructure in jets S. D. Ellis WC LHC Thy. Net. Work December 2006 34

LHC and BSM Goals • Many questions, but some answers from LHC Olympics learn about phenomenological challenges of LHC (a pedagogical tool) Study “Black Boxes” (BB) of simulated events containing unknown BSM signal that has been processed by realistic detector simulation (PGS), i. e. , events are lists of (sometimes mis-IDed and mismeasured) objects (leptons, photons, jets & MET) Try to ID the new physics – difficult even when no real SM background Jets play central role and PGS 3. 0 used cone jets, while PGS 4. 0 uses k. T jets - compare S. D. Ellis WC LHC Thy. Net. Work December 2006 35

Interesting comparison in context of LHC Olympics – new physics at few Te. V scale means highly boosted particles decay into 1, instead of 2 (or more jets) From Jon Walsh at KITP UW BB with 2 kinds of jets S. D. Ellis WC LHC Thy. Net. Work December 2006 36

Larger fluctuations in jet properties (# of charged tracks) with k. T algorithm S. D. Ellis WC LHC Thy. Net. Work December 2006 37

LHC environment May be much “noisier” at the LHC • Enhanced UE ? • Pile-up at large Luminosity – multiple events in each time bucket (most min-bias) S. D. Ellis WC LHC Thy. Net. Work December 2006 38

Studies from Matteo Cacciari & Gavin Salam Talk at MC@LHC 7/2006 S. D. Ellis WC LHC Thy. Net. Work December 2006 39

Z’ reconstruction – can fix with detailed jet-by -jet analysis! Need to verify can do this in real detector, i. e. , measure jet area S. D. Ellis WC LHC Thy. Net. Work December 2006 40

If New Physics New Jet Structure • E. g. , Produce particles in separate sector of theory, The Hidden Valley of Strassler [hep-ph/0607160, hep-ph/0605193, hep-ph/0604261] Decay back into SM particles with More jets Enhanced heavy flavor Displaced vertices (if long lifetimes) S. D. Ellis WC LHC Thy. Net. Work December 2006 41

Simulated (Strassler) Events – many b’s & jets M_Z’ = 3 Te. V 8 b’s M_Vpion = 30 Ge. V 3 jets Hidden Valley is 2 -flavor QCD-like S. D. Ellis WC LHC Thy. Net. Work December 2006 42

Some with taus & Missing ET 6 b’s & 2 taus 1 jet? S. D. Ellis WC LHC Thy. Net. Work December 2006 43

More b’s & messy jets 20 b’s S. D. Ellis WC LHC Thy. Net. Work December 2006 44

Displaced Jet Vertices S. D. Ellis WC LHC Thy. Net. Work December 2006 45

Summary • Iterative Cone jets have many issues, but they are the devils we know and can (largely) correct for. • k. T jets do not exhibit these devils, but may have their own, especially in the noisy LHC world. Can we learn to correct for them? • Can we tell SM jets from BSM jets? Is the subjet structure the answer? • Do we need a different analysis tool? S. D. Ellis WC LHC Thy. Net. Work December 2006 46

Extra Detail Slides S. D. Ellis WC LHC Thy. Net. Work December 2006 47

Dictionary of Hadron Collider Terminology EVENT HADRON-HADRON COLLISION Primary (Hard) Parton-Parton Scattering Initial-State Radiation (ISR) = Spacelike Showers associated with Hard Scattering Underlying Event Multiple Parton-Parton Interactions: Additional parton-parton collisions (in principle with showers etc) in the same hadron-hadron collision. = Multiple Perturbative Interactions (MPI) = Spectator Interactions Fragmentation Perturbative: Non-perturbative: Final-State Radiation (FSR) = Timelike Showers = Jet Broadening and Hard Final-State Bremsstrahlung String / Cluster Hadronization (Color Reconnections? ) Beam Remnants: Left over hadron remnants from the incoming beams. Colored and hence correlated with the rest of the event PILE-UP: Additional hadron-hadron collisions recorded as part of the same event. S. D. Ellis WC LHC Thy. Net. Work From Peter Skands December 2006

S. D. Ellis WC LHC Thy. Net. Work December 2006 49